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3. Powers with positive and negative exponents

The power operation is recorded as follows:

- base;

- exponent;

- the result of the increment or the value of the degree

Read as: "

$a$ to the power

$b$ equals

$c$ ".

Calculating a step value is called stepping!

If the magnifier is a natural number.

$\begin{array}{l} a^{n} = \underset{⏟}{a \cdot a \cdot a \cdot ... \cdot a} \\ n times \end{array}$

The positive value of a positive integer is always positive.

$3^{2} = 3 \cdot 3 = 9$

${(\frac{2}{5})}^{3} = \frac{2}{5} \cdot \frac{2}{5} \cdot \frac{2}{5} = \frac{8}{125}$

A negative number is positive if the multiplier is an even number and negative if the multiplier is an odd number.

${(- 3)}^{4} = (- 3) \cdot (- 3) \cdot (- 3) \cdot (- 3) = 81$

${(- 3)}^{3} = (- 3) \cdot (- 3) \cdot (- 3) = - 27$

Important!

Distinguish some seemingly similar notes

${(- 2)}^{4}$ and

$- 2^{4}$ . In the first case, the minus sign is the base sign

$(-2)$ and in the second case, the degree sign (base is

$2$ ).

${(- 2)}^{4} = (- 2) \cdot (- 2) \cdot (- 2) \cdot (- 2) = 16$

${- 2}^{4} = - (2 \cdot 2 \cdot 2 \cdot 2) = - 16$ .

Did you find an error?